3/8x-1/6x+5/12=69

Solution for 3/8x-1/6x+5/12=69 equation:

3/8x-1/6x+5/12=69

We move all terms to the left:

3/8x-1/6x+5/12-(69)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


determiningTheFunctionDomain
3/8x-1/6x-69+5/12=0

We calculate fractions


1440x^2/576x^2+216x/576x^2+(-96x)/576x^2-69=0

We multiply all the terms by the denominator


1440x^2+216x+(-96x)-69*576x^2=0

Wy multiply elements

1440x^2-39744x^2+216x+(-96x)=0

We get rid of parentheses

1440x^2-39744x^2+216x-96x=0

We add all the numbers together, and all the variables

-38304x^2+120x=0

a = -38304; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-38304)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-38304}=\frac{-240}{-76608}
=5/1596
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-38304}=\frac{0}{-76608}
=0
$